Analyzing Dynamics That Can Choke Supercomputers

http://www.computerworld.com/printthis/2005/0,4814,106722,00.html

Getting Real:

Analyzing Dynamics That Can Choke Supercomputers

Researchers find ways to tame the complexity in real-world reasoning

Future Watch by Gary H. Anthes , DECEMBER 05, 2005 (COMPUTERWORLD) -

It is surely one of the more mind-blowing PowerPoint slides ever created. It's a graph, and one of the smallest numbers, near the bottom of the vertical axis, is 10¹⁷, the number of seconds from now until the sun burns up. Then comes 10⁴⁷, the number of atoms on Earth. After that, the numbers get really big, topping the scale at 10 ^301,020.

This graph, from the Defense Advanced Research Projects Agency, shows the exponential growth in possible outcomes for a range of activities, from a simple car engine diagnosis with 100 variables to war gaming with 1 million variables (that's what the 10^301,020 represents).

The point DARPA is trying to make in explaining its Real-World Reasoning Project is that computers will never be able to exhaustively examine the possible outcomes of complex activities, any more than a roomful of monkeys with typewriters would ever be able to re-create the works of Shakespeare. But in the recently completed Phase I of the Real Project, as it's called, the agency did discover shortcuts that can tame the punishing combinatorial complexity that for decades has stymied efforts to model the real world.

Beyond Brute Force

Bart Selman, a computer science professor at Cornell University and one of three DARPA contractors on the project, points out that for a decade there have been automated reasoning tools that can discover defects in chip or software designs. These tools can "prove" the correctness of a specification without exhaustively testing every situation the chip or software might encounter.

But those tools can do only what's called single-agent reasoning. Selman is extending the concepts to a much harder class of problem -- multiagent scenarios in which there's one or more opposing forces -- and he's developed chess-playing software to test his ideas. The best chess programs today, such as IBM's Deep Blue, excel by brute-force trials of moves, analyzing millions of board positions per second. "Deep Blue explores hundreds of millions of strategies, but most of them are very dumb," Selman says. "Grandmasters only explore three or four possible lines of play."

The Cornell chess program works more like a grandmaster, he says. "It might exploit certain strategies, then find they are not successful. It learns from that and adds that to its knowledge base. It gets better the more games it plays, even during a single game," Selman explains. It develops a conceptual view of the board and seeks out overall positions that will give it strength.

By applying these learning techniques and other improvements over traditional reasoning tools, Selman's team has so far achieved a 10⁹ speed improvement over those tools, he says.

While Selman works on two-agent systems like chess, researchers at SRI International in Menlo, Park, Calif., are looking at games with four or more agents. That lets them include the dynamics of partnerships and coalitions often found in real-world conflicts.

Patrick Lincoln, director of the nonprofit's Computer Science Laboratory, has applied a "model checker" that's normally used to prove out semiconductor designs to a four-player variant of chess and to Diplomacy, a seven-player board game set in Europe just before World War I.

Lincoln developed an algorithm that can find the "Nash equilibrium" in a game, a point at which no player can deviate from his strategy without harming his outcome. Once that's been determined and the strategies of all the players are known, the model checker can find the best tactical moves given the various partnerships that have evolved. "This is a major computational challenge," Lincoln concedes.

Like Selman at Cornell, Lincoln has used model-checking techniques to mathematically prune the combinatorial tree. "We are doing it symbolically, in a way we don't have to exhaustively look at all the cases," he says.

Meanwhile, researchers at the University of California, Berkeley, are introducing notions of uncertainty into automated reasoning. They are modeling Kriegspiel chess, a variant of the game that the Prussian army used in the 19th century to train its officers. In Kriegspiel chess, neither opponent sees the pieces or the moves of the other, so each works only with information that's been inferred from the consequences of his own moves.

Stuart Russell, a computer science professor at Berkeley, says his team has come up with search algorithms that are 100 to 1,000 times faster than earlier methods for this kind of problem. Some can find solutions directly, without trying all possibilities. He says his techniques could one day be used in applications dealing with real-world situations whose dynamics are only partially observable, such as negotiations, management of traffic flows or supply distribution systems.

"With these technologies, one might create a logistics decision-support system that could, for instance, consider the likelihood of future events such as a natural disaster, and factor the event, and its implications, into the logistics process," says Tom Wagner, DARPA's program manager for the Real Project. "That same logistics system could also reason about the value of forming a relationship with another company, possibly even a competitor, as a way to improve the response to that disaster."

In the next phase of the project, not yet approved by DARPA, SRI will scale up the tools to handle more complex games with more players, Lincoln says. "The exponentials are so terrifying," he says. "The only way to make progress is to tame them algorithmically."